Quiz about Limit and continuity

Question 1

If $$\lim_{x\rightarrow0^+}f\left(x\right)=5$$ and $$\lim_{x\rightarrow0^-}\ f\left(x\right)=-5$$ , then $$\lim_{x\rightarrow0}\ f\left(x\right)=\left(\ \ \ \ \ \right)$$

Accepted Answer

$$Does\ not\ exist$$

Answer

$$5$$

Answer

$$-5$$

Answer

0

Question 2

Given that $$\lim_{x\rightarrow a}\ f\left(x\right)=4$$ and $$\lim_{x\rightarrow a}\ g\left(x\right)\ =\ -2$$ , find $$\lim_{x\rightarrow a}\left[3f\left(x\right)-\frac{1}{2}g\left(x\right)\right]^2$$

Accepted Answer

$$169$$

Answer

$$121$$

Answer

$$-121$$

Answer

$$-169$$

Question 3

$$\lim_{x\rightarrow-5^-}\ \frac{10}{x+5}$$

Accepted Answer

$$-\infty$$

Answer

$$\infty$$

Answer

Does not exist.

Question 4

$$\lim_{x\rightarrow1}\ \frac{2x^2-8x+6}{x^2-1}$$

Accepted Answer

$$-2$$

Answer

$$-1$$

Answer

Does not exist.

Question 5

$$\lim_{x\rightarrow0}\ \frac{2x}{3-\sqrt[]{x+9}}$$

Accepted Answer

$$-12$$

Answer

$$0$$

Answer

Does not exist.

Answer

$$-6$$

Question 6

The $$\lim_{x\rightarrow a}\ y$$ does not exist. True or False?

Accepted Answer

False

Answer

True

Question 7

$$\lim_{x\rightarrow\infty\ }\ \frac{2x+1}{1-x^3}$$

Accepted Answer

$$0$$

Answer

$$-2$$

Answer

$$2$$

Answer

$$\infty$$

Question 8

$$\lim_{x\rightarrow\infty}\ \sqrt[]{\frac{20x^4-2x^2}{5x^4+4}}$$

Accepted Answer

$$2$$

Answer

$$0$$

Answer

$$4$$

Answer

$$\infty$$

Question 9

$$Based\ on\ the\ graph\ given,\ find\ \lim_{x\rightarrow0}\ f\left(x\right).$$

Accepted Answer

Does not exist.

Answer

$$-\infty$$

Answer

$$0$$

Answer

$$1$$

Question 10

Is f(x) continuous at x = a?

Accepted Answer

No

Answer

Yes

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